Active camera not working on blender game
There's several issues on you file...

Character Structure

Try to read the BGE Guide To Character Setup, you will understand that an armature should not be the physics object of your character: make an physics object with physics type Capsule and parent the armature to it. Also, make sure to check the Actor checkbox, so your player can be detected by the zones.



Zones Physics

Static objects can't detect collisions, so you have to change your zones physics types to Sensor and enable Detect actors. Also, disable the pulse mode on the collision sensors, it takes a lot of memory.



A Silly Mistake...

Your collision sensors are looking for an object with the property Player, but your player does not have this property! Add it to your player and the sensors should detect it.



Conclusion

Also, there's a lot of optimization you could do, especially disabling the physics on objects that don't need it (paintings, lamps, statue, etc). Try to read these guides to learn a bit more about logic, structure and project management.

Your file with some of the issues corrected: